Calculator with Pi (π) UK 2025 - Free Circle & Sphere Calculator
Free calculator with Pi (π) for UK students. Calculate circle area, circumference, sphere volume, cylinder calculations, and more.
Last updated: February 2026
Calculator with Pi (π) - Free Circle & Sphere Calculator UK
Our free calculator with Pi (π) helps you perform all circle, sphere, cylinder, and cone calculations instantly. Whether you're working on GCSE maths homework, revising for A-Level exams, or solving geometry problems, this comprehensive Pi calculator provides accurate results with step-by-step explanations. Calculate circle area, circumference, sphere volume, surface area, and more - all completely free with no registration required.
The ratio of a circle's circumference to its diameter
Circle Calculator
Sphere Calculator
Cylinder Calculator
Cone Calculator
General π Calculator
Perform any calculation involving Pi. Use 'p' or 'pi' for π.
Quick Examples:
- Circle area:
pi * 5^2(radius 5) - Circumference:
2 * pi * 7(radius 7) - Sphere volume:
(4/3) * pi * 3^3(radius 3)
Pi (π) Quick Reference
Pi to Various Decimal Places
| Decimal Places | Value | Common Usage |
|---|---|---|
| 2 dp | 3.14 | Quick estimates |
| 3 dp | 3.142 | GCSE calculations |
| 5 dp | 3.14159 | A-Level calculations |
| 10 dp | 3.1415926536 | Scientific work |
| Fraction | 22/7 ≈ 3.143 | Mental calculations |
Essential Pi Formulas for GCSE & A-Level
Circle
Area = πr²
Circumference = 2πr = πd
Arc length = (θ/360) × 2πr
Sector area = (θ/360) × πr²
Sphere
Volume = (4/3)πr³
Surface Area = 4πr²
Cylinder
Volume = πr²h
Curved Surface = 2πrh
Total Surface = 2πr(r + h)
Cone
Volume = (1/3)πr²h
Curved Surface = πrl
Slant height l = √(r² + h²)
Worked Examples (GCSE Style)
Example 1: Circle Area
Question: A circular pond has a radius of 4 metres. Calculate the area of the pond. Give your answer to 2 decimal places.
Solution:
- Identify the formula: Area = πr²
- Substitute the radius: Area = π × 4²
- Calculate: Area = π × 16
- Area = 50.2654...
- Answer: 50.27 m² (2 dp)
In terms of π: Area = 16π m²
Example 2: Sphere Volume
Question: A basketball has a diameter of 24 cm. Calculate the volume of air it can hold. Give your answer to 3 significant figures.
Solution:
- Find the radius: r = 24 ÷ 2 = 12 cm
- Identify the formula: Volume = (4/3)πr³
- Substitute: Volume = (4/3) × π × 12³
- Calculate: Volume = (4/3) × π × 1728
- Volume = 7238.229...
- Answer: 7240 cm³ (3 sf)
Example 3: Cylinder Surface Area
Question: A cylindrical can has radius 5 cm and height 12 cm. Find the total surface area.
Solution:
- Formula: Total Surface Area = 2πr(r + h)
- Substitute: TSA = 2 × π × 5 × (5 + 12)
- Calculate: TSA = 2 × π × 5 × 17
- TSA = 170π = 534.07...
- Answer: 534.07 cm² (or 170π cm² in exact form)
Tips for Pi Calculations
1. Use the Calculator π Button
Always use your calculator's π button rather than typing 3.14 for more accurate results. The π button stores many more decimal places.
2. Check Radius vs Diameter
Questions often give diameter instead of radius. Remember to divide by 2 if you need the radius. This is a common source of errors.
3. Know When to Leave in Terms of π
If a question asks for an exact answer, leave it as 16π rather than 50.27. Look for phrases like "in terms of π" or "exact answer".
4. Units Matter
Area is in square units (cm², m²), volume is in cubic units (cm³, m³). Make sure your answer has the correct units.
5. Memorise Key Formulas
Learn the formulas for area, circumference, and volume. Some exam boards provide formula sheets, others don't - check your specification.
6. Estimate First
Use π ≈ 3 for quick estimates. If the area of a circle with r=10 gives you 3140, that's about right (π × 100 ≈ 300).
Common Mistakes to Avoid
Using Diameter Instead of Radius
Wrong: Area = π × 10² = 314 when diameter is 10
Right: If d=10, then r=5, so Area = π × 5² = 78.5
Forgetting to Square or Cube
Wrong: Area = πr = π × 5 = 15.7
Right: Area = πr² = π × 5² = 78.5
Wrong Units
Wrong: Area of circle = 50.27 cm
Right: Area of circle = 50.27 cm² (area needs square units)
Premature Rounding
Wrong: Using 3.14 throughout then rounding
Right: Use π button, only round final answer to required dp/sf
Frequently Asked Questions
Pi (π) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It's approximately 3.14159, but the digits continue infinitely without repeating (it's an irrational number).
Pi is fundamental to geometry and appears in countless mathematical and scientific formulas. It's used to calculate:
- Circle areas and circumferences
- Volumes and surface areas of spheres, cylinders, and cones
- Trigonometric functions
- Wave equations in physics
- Probability and statistics
The area of a circle is calculated using: Area = πr²
Steps:
- Identify the radius (r). If given diameter, divide by 2
- Square the radius (multiply it by itself)
- Multiply by π (use your calculator's π button)
- Round to the required number of decimal places or significant figures
Example: Circle with radius 6 cm
Area = π × 6² = π × 36 = 113.10 cm²
Circumference is the distance around the outside edge of a circle (perimeter). It's measured in linear units (cm, m, etc.).
Area is the space inside the circle. It's measured in square units (cm², m², etc.).
Formulas:
- Circumference = 2πr = πd
- Area = πr²
For a circle with radius 5 cm: Circumference = 31.42 cm, Area = 78.54 cm²
Leave your answer in terms of π when:
- The question specifically asks for an exact answer
- The question says "in terms of π" or "give an exact answer"
- You're finding an intermediate value that you'll use in further calculations
Examples of answers in terms of π:
- Area = 16π cm² (rather than 50.27 cm²)
- Volume = 36π cm³ (rather than 113.10 cm³)
If the question asks for a numerical answer to a certain number of decimal places, calculate the decimal value.
The volume of a sphere is: V = (4/3)πr³
Steps:
- Find the radius (if given diameter, divide by 2)
- Cube the radius (r × r × r)
- Multiply by π
- Multiply by 4/3 (or equivalently, multiply by 4 then divide by 3)
Example: Sphere with radius 3 cm
V = (4/3) × π × 3³ = (4/3) × π × 27 = 36π = 113.10 cm³
For GCSE maths, you should know these key formulas:
- Circle area: A = πr²
- Circumference: C = 2πr or C = πd
- Arc length: L = (θ/360) × 2πr
- Sector area: A = (θ/360) × πr²
- Sphere volume: V = (4/3)πr³
- Sphere surface area: A = 4πr²
- Cylinder volume: V = πr²h
- Cone volume: V = (1/3)πr²h
Note: Some exam boards provide a formula sheet, others require you to memorise formulas. Check your specification.
To find radius from area, rearrange the formula:
- Start with: Area = πr²
- Divide both sides by π: Area/π = r²
- Take the square root: r = √(Area/π)
Example: Circle has area 100 cm². Find the radius.
r = √(100/π) = √31.83... = 5.64 cm
Pi Day is celebrated on March 14th (3/14 in American date format) because the date represents the first three digits of Pi: 3.14.
The holiday was first recognized in 1988 at the San Francisco Exploratorium. In 2009, the US House of Representatives officially designated March 14 as National Pi Day.
Pi enthusiasts sometimes celebrate at 1:59 PM on this day to represent 3.14159, and may even extend it to 3/14/15 at 9:26:53 AM for even more digits!
Official UK Maths Resources
BBC Bitesize - Circles
GCSE circle calculations with videos and interactive activities.
Maths Genie - GCSE Revision
Free worksheets and worked examples for circle and sphere problems.
Corbett Maths
Video tutorials and practice questions on circles and 3D shapes.
Math is Fun - Pi
Interactive explanation of Pi with history and interesting facts.
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About This Calculator with Pi
Our free calculator with Pi (π) has been designed specifically for UK students studying GCSE and A-Level mathematics. It provides instant, accurate calculations for all circle, sphere, cylinder, and cone problems you'll encounter in your studies.
The calculator features five specialized modes:
- Circle Calculator: Calculate area and circumference from radius, diameter, or work backwards from known values
- Sphere Calculator: Find volume and surface area of spheres
- Cylinder Calculator: Calculate volume, curved surface area, and total surface area
- Cone Calculator: Calculate volume, slant height, and curved surface area
- General π Calculator: Evaluate any expression involving Pi
This calculator uses JavaScript's Math.PI constant which provides Pi to 15 decimal places, ensuring your calculations are accurate to more precision than any exam requires. Results can be displayed as decimal values or you can easily express them in terms of π for exact answers.
Whether you're doing homework, revising for exams, or checking your working, this calculator provides step-by-step results with clear explanations to help you understand the mathematics behind each calculation.
Expert Reviewed — This calculator is reviewed by our team of financial experts and updated regularly with the latest UK tax rates and regulations. Last verified: February 2026.
Last updated: February 2026 | Verified with latest UK rates
Pro Tips for Accurate Results
- Double-check your input values before calculating
- Use the correct unit format (metric or imperial)
- For complex calculations, break them into smaller steps
- Bookmark this page for quick future access
Understanding Your Results
Our Calculator With Pi provides:
- Instant calculations - Results appear immediately
- Accurate formulas - Based on official UK standards
- Clear explanations - Understand how results are derived
- 2025/26 updated - Using current rates and regulations
Common Questions
Is this calculator free?
Yes, all our calculators are 100% free to use with no registration required.
Are the results accurate?
Our calculators use verified formulas and are regularly updated for accuracy.
Can I use this on mobile?
Yes, all calculators are fully responsive and work on any device.
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